Is it possible to make physics respond to the effective mesh after a displacement material has been applied?
Unfortunately that isn't possible - the 'Bump and Displacement' option (by connecting the 'Displacement' socket on the Material Output node) operates on the rendered result only - simulations cannot access the displaced geometry.

In order for smulations such as Rigid Body physics to be able to take account of displacement you need to use a Displacement modifier and set the rigid body collision settings set to enable 'Deforming' (by setting the 'Mesh' shape Source to 'Final' (All modifiers)).